In … "A Theoretical Framework for Monetary Analysis," I outlined a simple model of six equations in seven variables that was consistent with both the quantity theory of money and the Keynesian income-expenditure theory…The difference between the two theories is in the missing equation the quantity theory adds an equation stating that real income is determined outside the system (the assumption of "full employment"); the income-expenditure theory adds an equation stating that the price level is determined outside the system (the assumption of price or wage rigidity)…The present addendum to my earlier paper suggests a third way to supply the missing equation. This third way involves bypassing the breakdown of nominal income between real income and prices and using the quant ity theory to derive a theory of nominal income rather than a theory of either prices or real income.
In my view, "the Phillips curve" is not a theory of how prices influence output or output influences prices, but rather how nominal income influences output and prices. Generally, it is output and prices together in the short run, and then prices only in the long run.
There is nothing unusual about that approach, and having money determine output in period t+1 and then inflation in period t+2 seems like a simple way to illustrate this concept. Of course, if the model shows that a situation where nominal income remains unchanged (or on a constant growth path,) so that there are no fluctuations in nominal income, the process by which the short run/long run relationship is modeled generates fluctuations in real output and prices, simply shows that the model is flawed.